This paper considers chatter in diamond turning of aluminum. A nonlinear chip area model is developed for use with the classic single degree of freedom cutting model. The chip area model is formulated as a function of the change in depth of cut between consecutive passes. This function is shown to be highly dependent on the quadratic term when turning the diameter of cylindrical workpieces with round-nosed diamond tools. The cutting model is further extended to include an impact disturbance to the cutting process. The recent research in ultra-precision machining is incorporated to properly account for the rise in specific cutting energy at extremely light depths of cut. Simulations of the resulting tool displacement show close agreement with experimental measurements.
Issue Section:
Research Papers
1.
El Baradie
M. A.
1993
, “Statistical Analysis of the Dynamic Cutting Coefficients and Machine Tool Stability
,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 115
, pp. 205
–214
.2.
Hannah, N. H., and Tobias, S. A., 1974, “A Theory of Nonlinear Regenerative Chatter,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY, pp. 247–255.
3.
Lucca, D., et al., 1991, “Energy Dissipation in Ultra-Precision Machining of Copper,” Annals of CIRP, Vol. 40-1-91.
4.
Lucca
D.
1994
, “Energy Dissipation and Tool Workpiece Contact in Ultra-Precision Machining
,” Trib. Transactions
, Vol. 37
, pp. 651
–655
.5.
Kasahara
N.
Sato
H.
Tani
Y.
1992
, “Phase Characteristics of Self-Excited Chatter in Cutting
,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 114
, pp. 393
–399
.6.
Minis
I. E.
Magrab
E. B.
Pandelidis
I. O.
1990
, “Improved Methods for the Prediction of Chatter in Turning, Part 1: Determination of Structural Response Parameters
,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 112
, pp. 12
–20
.7.
Minis
I. E.
Magrab
E. B.
Pandelidis
I. O.
1990
, “Improved Methods for the Prediction of Chatter in Turning, Part 2: Determination of Cutting Process Parameters
,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 112
, pp. 21
–27
.8.
Minis
I. E.
Magrab
E. B.
Pandelidis
I. O.
1990
, “Improved Methods for the Prediction of Chatter in Turning, Part 3: A Generalized Linear Theory
,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 112
, pp. 28
–35
.9.
Press, W. G., et al., 1990, Numerical Recipes in C, Cambridge University Press, Cambridge.
10.
Stepan, G., 1989, Retarded Dynamical Systems: Stability and Characteristic Functions, Longman Scientific and Technical U.K. Limited, pp. 137–147.
11.
Thompson, R. A., 1980, “A General Theory for Regenerative Stability,” Proc.8th North American Manufacturing Research Conference (NAMRC), Univ. of Missouri, Rolla, MO, pp. 377–387.
12.
Thompson
R. A.
1988
, “Chatter Growth—Tests to Evaluate the Theory
,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY
, Vol. 110
, pp. 344
–351
.13.
Tlusty, J., and Heczko, M., 1980, “Improving Tests of Damping in the Cutting Process,” Proc. 8th North American Manufacturing Research Conference (NAMRC), Univ. of Missouri, Rolla, MO, pp. 372–376.
14.
Tlusty
J.
Ismail
F.
1981
, “Basic Non-Linearity in Machining Chatter
,” Annals of the CIRP
, Vol. 30
, No. 1
, pp. 299
–304
.15.
Tlusty, J., and Rao, B. S., 1978, “Verification and Analysis of Some Dynamic Cutting Force Coefficient Data,” Proc. 6th North American Manufacturing Research Conference (NAMRC), Univ. Of Florida, FL, pp. 420–426.
16.
Tlusty, J., 1985, “Machine Dynamics,” Handbook of High Speed Machining Technology, R. I. King, ed., Chapman and Hall, New York.
17.
Wu, D. W., and Liu, C. R., 1985, “An Analytical Model of Cutting Dynamics. Part 1: Model Building,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY, Vol. 107.
18.
Wu, D. W., and Liu, C. R., 1985, “An Analytical Model of Cutting Dynamics. Part 2: Verification,” ASME JOURNAL OF ENGINEERING FOR INDUSTRY, Vol. 107.
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